Question: Jessica is 6 years older than Kevin. Nineteen years ago, Jessica was 4 times as old as Kevin. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Kevin. Let Jessica's current age be $j$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $j = k + 6$ Nineteen years ago, Jessica was $j - 19$ years old, and Kevin was $k - 19$ years old. The information in the second sentence can be expressed in the following equation: $j - 19 = 4(k - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = k + 6$ . Substituting this into our second equation, we get the equation: $(k + 6)$ $-$ $19 = 4(k - 19)$ which combines the information about $k$ from both of our original equations. Simplifying both sides of this equation, we get: $k - 13 = 4 k - 76$ Solving for $k$ , we get: $3 k = 63$ $k = 21$.